Why it is hard to share the wealth

The rich are getting richer while the poor remain poor. If you doubt it, ponder these numbers from the US, a country widely considered meritocratic, where talent and hard work are thought to be enough to propel anyone through the ranks of the rich. In 1979, the top 1% of the US population earned, on average, 33.1 times as much as the lowest 20%. In 2000, this multiplier had grown to 88.5. If inequality is growing in the US, what does this mean for other countries?

Almost certainly more of the same, if you believe physicists who are using new models based on simple physical laws to understand the distribution of wealth. Their studies indicate that inequality in market economies may be very hard to get rid of.

Economists will join physicists to discuss these issues next week in Kolkata, India, at the first ever conference on the "econophysics" of wealth distribution. "We are interested in understanding whether there is some kind of social injustice behind this skewed distribution," says Sudhakar Yarlagadda of the Saha Institute of Nuclear Physics (SINP) in Kolkata.

It is well known that wealth is shared out unfairly. "People on the whole have normally distributed attributes, talents and motivations, yet we finish up with wealth distributions that are much more unequal than that," says Robin Marris, emeritus professor of economics at Birkbeck, University of London.

Pareto's law

In 1897, a Paris-born engineer named Vilfredo Pareto showed that the distribution of wealth in Europe followed a simple power-law pattern, which essentially meant that the extremely rich hogged most of a nation's wealth (New Scientist print edition, 19 August 2000). Economists later realised that this law applied to just the very rich, and not necessarily to how wealth was distributed among the rest.

Now it seems that while the rich have Pareto's law to thank, the vast majority of people are governed by a completely different law. Physicist Victor Yakovenko of the University of Maryland in College Park, US, and his colleagues analysed income data from the US Internal Revenue Service from 1983 to 2001.

They found that while the income distribution among the super-wealthy - about 3% of the population - does follow Pareto's law, incomes for the remaining 97% fitted a different curve - one that also describes the spread of energies of atoms in a gas (see graphic).

Gas analogy

In the gas model, people exchange money in random interactions, much as atoms exchange energy when they collide. While economists' models traditionally regard humans as rational beings who always make intelligent decisions, econophysicists argue that in large systems the behaviour of each individual is influenced by so many factors that the net result is random, so it makes sense to treat people like atoms in a gas.

The analogy also holds because money is like energy, in that it has to be conserved. "It's like a fluid that flows in interactions, it's not created or destroyed, only redistributed," says Yakovenko.

Yakovenko also found that the total income of those in the poorer part of the distribution did not change significantly with time after accounting for inflation. But incomes for those in the Pareto curve shot up nearly five times from 1983 to 2000, before declining with the US stock market crash of 2001.

Class jumping

This, along with research data from other countries, suggests that there are two economic classes. In one, the rich grow richer while in the other the poor stay poor. Yakovenko explains this by going back to the analogy of atoms in a gas.

The atoms assume an exponential distribution of energy when they are in thermal equilibrium, and pushing the gas away from this state takes a lot of energy and it could prove similarly difficult to shift an economy to a different state. Randomness in the model does, however, mean that individuals can jump from one class to another.

"It suggests that any kind of policy will be very inefficient," says Yakovenko. It would be very difficult to impose a policy to redistribute wealth "short of getting Stalin", says Yakovenko, who will talk in Kolkata next week.

Saving plans

A more sophisticated model developed by Bikas Chakrabarti of the SINP and his colleagues paints a slightly less bleak picture for the poor. His team adjusted the gas model to allow people to save various proportions of their money.

This model predicts both the wealth classes that Yakovenko found. It also suggests that if you save more you are more likely to end up rich, although there are no guarantees. Changing people's saving habits could be an effective way of making the wealth distribution fairer, rather than enforcing taxes, says Chakrabarti, who is one of the Kolkata conference organisers.

Macroeconomist Makoto Nirei at Utah State University in Logan, US, whose own work will be presented at the conference, is supportive of the physicists' work but he has reservations about how they model the exchange of money. "The model seems to me not like an economic exchange process, but more like a burglar process. People randomly meet and one just beats up the other and takes their money."

Other economists warn it is too early to use such models to inform policies. "The models are too abstract," says Thomas Lux, an economist at the University of Kiel in Germany. But J. Doyne Farmer, a physicist from the Santa Fe Institute in New Mexico, US, points out that these models have their place: "Many economic theories don't even come close to producing the wealth distribution we see, and if you can't produce that you're dead in the water."

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